What are
Dandelin constructions?
Mastery of the conic
sections hones a student's skills for
Calculus. In particular, the circle,
ellipse, parabola and hyperbola present a clear
opportunity for students to learn algebra,
graphing, vocabulary and definitions.
The Dandelin definitions and constructions are an
enrichment, or refinement, of the conics that
involve first placing a sphere inside a
cone. [Look above at the animations.]
If a cone is intersected by a plane, then the foci
of the conics are all points where the plane
touches the inscribed sphere. This is true
for all four conics.
Germinal Pierre Dandelin (1794 - 1847) published
this discovery when he was only 28 years old and
having already lived through extremely difficult
times. As an 18 year old Belgium student
studying in the elite Ecole Polytechnic in Paris,
he volunteered to serve in Napoleon's army.
When the advancing armies of Britain, Russia,
Austria and Prussia forced Napoleon to retreat to
Paris, Dandelin was wounded. He was one
month short of this 20th birthday. He would
spend the next eight years working as an engineer
in the Ministry of Interior, returning to Belgium
and becoming a citizen of the Netherlands.
While investigating the conics launched his career
as a mathematician, he would later publish in
stereographic projections, statics, algebra and
probability. In particular, his method of
approximating roots of an equation is now known as
the Dandelin-Graffe method.
